Mesh with full weight moves less than bone, and moves another mesh with no weight
In edit mode, if you select a vertex you can read - in the "N" panel - all the weighted bones, so to understand why the vertex is moving that way: if you want the vertex to move exactly with a bone it should be weighted to that bone only (even if the weight is not full 1.0).
If this does not resolve the problem I think you should upload the file.